Why does the shape keys shrink my mesh
It's hard to say from the information posted in your question since you don't have any screenshots or files attached, but I'm going to guess that the shape keys are behaving as they should, and you just aren't fully aware of how shape keys work. It's very common among people starting with shape keys to assume that the key will take into account how you transformed the mesh when you edited it. However, that isn't how they work.

Shape keys simply translate each vertex in a straight line from the original position to the modified position. This can result in undesired deformation if you are trying to make a shape key do something it shouldn't be used for. The purpose of shape keys is (most often) to correct deformation or add small details to the deformation of an object. I've seen many people use shape keys to animate eyelids, and I don't think it's the best way.

I would suggest using an armature to animate the eyelids, as you will be able to make the eyelid follow the curve of the eye properly. This does take a bit more time to setup, and is more complex, but the result is worth it as the eyelids will deform much better, as well as knowing how to rig an eyelid is a great skill to have. There are a number of tutorials on this that can help you get started, such as this one here: https://www.youtube.com/watch?v=CCGekumdLLU.